1. Field
The embodiments discussed herein are related to the warp analysis of a multilayer substrate.
2. Description of the Related Art
A multilayer substrate made of a plurality of substrates is warped in a process in which a thermal load is applied to the substrate. Such a process may be a reflow soldering process, The causes of the warp include a wiring pattern and a wiring ratio of each wiring layer, the arrangement of interlayer vias which are plating holes connecting between the layers in the multilayer substrate, the arrangement of solder resist, the arrangement of standard size perforated lines, and the like. The warp is predicted by using numerical simulation utilizing the warp analysis, and the prediction is fed back to the design of the multilayer substrate. As a result, it is possible to design the multilayer substrate with less warp.
Further, in the warp analysis, there is known a technique to generate, on the basis of wiring CAD (Computer Aided Design) data, the arrangement of interlayer vias, the arrangement of solder resist, and the arrangement of standard size perforated lines. The CAD data is design information of the multilayer substrate, i.e. structural analysis mesh (hereinafter referred to as FE (Finite Element) mesh) data in which there are reflected the wiring pattern for each wiring layer.
In the following, the generation of the conventional FE mesh will be described with reference to the accompanying drawings. FIG. 16 to FIG. 18 are figures showing a method for generating the conventional FE mesh.
First, as shown in FIG. 16, a wiring shape (positions of conductor and air in FIG. 16) is divided into lattice-shaped grids on the basis of wiring CAD data. Next, as shown in FIG. 17, a FE mesh made of a predetermined number of grids is prepared, so that the content of the conductor or the air (hole) in the FE mesh is calculated. Then, as shown in FIG. 18, the FE mesh whose calculated content is equal to or greater than a predetermined threshold value is determined as a portion where the conductor or air exists. Conventionally, the warp analysis has been performed on the basis of the FE mesh generated in this way.
Japanese Laid-open Patent Publication No. 2004-13437 discloses a technique in which a plurality of n elements that have arbitrary shapes is created. The plurality of n elements is used to divide a multilayer wiring substrate into a plurality of regions on the basis of model data representing the external shape, and the like, of the multilayer wiring substrate. Data of wiring pattern P formed in the multilayer wiring substrate are then compared to the respective n elements so that a ratio occupied by the wiring pattern P is calculated for each layer and each element on the basis of a residual copper ratio. A warp analysis of the multilayer wiring substrate is then performed on the basis of the residual copper ratio of each element and on the basis of mechanical physical property values of each element.
Japanese Laid-open Patent Publication No. 2006-39692 discloses a technique in which a single layer model is generated for each layer of an analysis object formed by laminating plate-shaped bodies, each having a non-uniform in-layer material, on the basis of the external shape of the analysis object and the composition of the each layer. A laminated shell model is generated from the single layer model for the each layer of the analysis object by using thickness information of the each layer. A neutral surface is calculated from the laminated shell model. A deformed neutral surface is calculated by applying a boundary condition to the neutral surface, and a deformation of the laminated shell model is calculated by using the deformation of the neutral surface and the thickness information.